Practice Examples Of Antisymmetric Relations (17.4.2)

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6 sample questions

Question 1.
Define an antisymmetric relation.
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Think about the implication of pairs in a relation.
Question 2.
Is the relation R = {(1, 2)} antisymmetric?
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Look for the reverse pair.
3Question 3.
What defines an antisymmetric relation?
- If a relates to b and b to a
- a must equal b
- If a relates to b
- then b relates to a
- None of the above
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Think about the implications of pairs being equal.
4Question 4.
Is the relation R = {(1, 1), (1, 2)} antisymmetric?
- True
- False
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Identify if both pairs exist.
Question 5.
Define whether R = {(1, 1), (2, 2), (3, 3), (1, 2)} is antisymmetric. Explain your reasoning.
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Look for pairs that might contradict.
Question 6.
Create a set of relations R on {a, b, c} such that R is antisymmetric but contains both (a, b) and (b, a). Can this be done? Discuss why or why not.
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Reflect on properties governing antisymmetry.

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